Spin and Orbital Magnetic Response on the Surface of a Topological Insulator

TL;DR

This paper explores how spin and orbital magnetic responses on a topological insulator's surface influence magnetic textures, revealing universal scaling behaviors and magnetoelectric couplings relevant for spintronics.

Contribution

It introduces a theoretical framework linking Dirac electron magnetization to magnetic textures and uncovers universal scaling laws for Dzyaloshinski-Moriya interactions.

Findings

Persistent currents induce Dzyaloshinski-Moriya interactions.

Orbital motion creates magnetoelectric coupling.

Universal scaling form of interactions as a function of temperature and chemical potential.

Abstract

Coupling of the spin and orbital degrees of freedom on the surface of a strong three-dimensional insulator, on the one hand, and textured magnetic configuration in an adjacent ferromagnetic film, on the other, is studied using a combination of transport and thermodynamic considerations. Expressing exchange coupling between the localized magnetic moments and Dirac electrons in terms of the electrons' out-of-plane orbital and spin magnetizations, we relate the thermodynamic properties of a general ferromagnetic spin texture to the physics in the zeroth Landau level. Persistent currents carried by Dirac electrons endow the magnetic texture with a Dzyaloshinski-Moriya interaction, which exhibits a universal scaling form as a function of electron temperature, chemical potential, and the time-reversal symmetry breaking gap. In addition, the orbital motion of electrons establishes a direct magnetoelectric coupling between the unscreened electric field and local magnetic order, which furnishes complex long-ranged interactions within the magnetic film.